Question: Simplify the following expression: $n = \dfrac{-2y^2 + 4y + 96}{y - 8} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ n =\dfrac{-2(y^2 - 2y - 48)}{y - 8} $ Then we factor the remaining polynomial: $y^2 {-2}y {-48} $ ${-8} + {6} = {-2}$ ${-8} \times {6} = {-48}$ $ (y {-8}) (y + {6}) $ This gives us a factored expression: $\dfrac{-2(y {-8}) (y + {6})}{y - 8}$ We can divide the numerator and denominator by $(y + 8)$ on condition that $y \neq 8$ Therefore $n = -2(y + 6); y \neq 8$